A known conventional cosmetic material applying container discharges cosmetic material filled in a filling region inside of the container from a leading end portion formed of soft material as described in, for example, Patent Document 1. In this cosmetic material applying container, the leading end portion is formed to have an outer shape of a transverse cross section in a flat shape and an edge shape in a side view. The leading end portion includes a top end surface that constitutes an applying surface. The applying surface includes a distal end where a vertex position is formed.